Homework Quiz In a randomly selected class at OHS (Mr. Llorens’ Stats class) , the following data is obtained regarding the current grades of students: What is the probability of selecting a boy, or someone that is failing? Boys Girls Passing 3 4 Failing 12 11

The Multiplication Rule Section 4-4

Multiple Events So far, we have considered the probability of a single event and compound events. Now we are going to start looking at the probability of multiple events occurring.

2. Who said that “smoking is one of the leading causes of statistics”? Example Consider a 2 question quiz that you know nothing about. The first question is true/false, and the second question is multiple choice. What is the probability of getting both answers correct? 1. True or false: A pound of feathers weighs more than a pound of gold. 2. Who said that “smoking is one of the leading causes of statistics”? Philip Morris Smokey Robinson Fletcher Knebel R.J Reynolds Virginia Slims

Tree Diagram

P(A and B) = P(A) X P(B) Multiplication Rule This is different than last section, as we are now considering the likelihood of event A and event B occurring in succession (one after the other). NOT both occurring in the same event This rule might change slightly based on something we will learn later in the lesson

Example You enter a raffle at both the Oswego and Oswego East (trader) football games. You are among the 202 people to enter the OHS raffle, and the 168 people to enter the OEHS raffle. What is the probability of winning both raffles?

Conditional Probability P(B|A) [pronounced B given A] the probability that event B occurs given that event A has already occurred.

Example Assume that you enter the same raffle at OHS (202 people entered including yourself), but this time two winners are chosen. Given that your ticket was not pulled first, what is the probability yours is second?

Independent Events If event A has no effect on event B, then A and B are considered to be independent. In that case we know: P(B|A) = P(B)

Independent or Dependent Events? Finding out that you left your homework in your locker. Finding out that your pencil needs to be sharpened.

Independent or Dependent Events? Casey wearing a One Direction t-shirt. Casey asking someone on a date and getting a positive response.

Independent or Dependent Events? Randomly selecting a consumer who owns a cat. Randomly selecting a consumer who owns kitten mittens.

Homework P.168: 5-12

The Multiplication Rule Section 4-4

Independent or Dependent Events? Bobby watches the Simpson’s on T.V. Bobby then watches Honey Boo Boo on T.V.

Independent or Dependent Events? Discovering you left your car’s headlights on. Discovering that your car’s battery is dead.

Independent or Dependent Events? Randomly selecting someone who is vegan. Randomly selecting someone who has a salad for lunch.

How does conditional probability effect our formula for P(A and B)? Critical Question! How does conditional probability effect our formula for P(A and B)?

Applying the Multiplication Rule

Example Genetics Experiment Mendel’s famous hybridization experiments involved peas, like those shown in the image below. If two of the peas shown in the figure are randomly selected without replacement, find the probability that the first selection has a green pod and the second has a yellow pod.

Example A medical researcher is evaluating pacemakers. He is going to choose two from a pool of 3 good and 2 bad pacemakers. What is the probability of choosing a good one first, followed by a bad one [without replacement]? Is this different from the probability of choosing a bad one first, followed by a good one?

Example Consider two randomly selected people. What is the probability that both people are born on the same day of the week? What is the probability that they are both born on a Monday?

Trasketball RETURNS Swoosh!!!!!!!!!!!!!!!!!!!!!!! (~You Wish~)

Foul Shot! The Wheeling Tire Company produced a batch of 5,000 tires that includes exactly 200 that are defective. If 4 tires are randomly selected for installation on a car, what is the probability that they are all good? 0.849

Yes, there is a very small chance that all 100 tires are good. TWO Pointer The Wheeling Tire Company produced a batch of 5,000 tires that includes exactly 200 that are defective. If 100 tires are randomly selected for shipment to an outlet, what is the probability that they are all good? Should this outlet plan to deal with defective tires returned by consumers? 0.017. Yes, there is a very small chance that all 100 tires are good.

Half-Court Shot The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that your alarm clock has a 0.900 probability of working on any given morning. What is the probability that your alarm clock will not work on the morning of an important final exam? 0.100

Buzzer Ball The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that your alarm clock has a 0.900 probability of working on any given morning. If you have two such alarms, what is the probability that they both fail on the morning of an important final? 0.01.

Slam Dunk! The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that your alarm clock has a 0.900 probability of working on any given morning. With one alarm clock you have a 0.9 probability of being awakened. What is the probability of being awakened if you use two alarm clocks? 0.99

Homework P.168-169 #17-19, 21